Question

Below, the two-way table is given for a class
of students.
Sophomore
Freshmen
4
3
6
4
Juniors Seniors Total
2
6
Male
Female
Total
If a male student is selected at random, what is the
probability the student is a freshman.
2
3
P (Freshman | Male) = [?]%
Round to the nearest whole percent.
Enter

Answer 1

Answer:

2/7 = 29% (nearest percent)

Step-by-step explanation:

Calculate the totals and add them to the table:

$\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}$

Probability Formula

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student is male

Use the given table to calculate the probability that the student is male:

$\sf \implies P(B)=\dfrac{14}{30}$

And the probability that the student is a freshman and male:

$\implies \sf P(A \cap B)=\dfrac{4}{30}$

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$

Substitute the found values into the formula:

$\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%$

Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).

Learn more about conditional probability here:

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